藉由應力波量測材料性質是一古老且快速的實驗力學方法,除了傳統量測應力脈沖波(Pulse)之波速,以決定材料之彈性常數外,共振超音波實驗可精確地量測材料之黏 彈性質及異向性彈性常數。本文以高階有限差分之數值計算方式(RUS code),模擬二 維材料之共振超音波實驗,於試體的一個角落,以Ricker wavelet 為輸入波函數,模擬 脈沖波,並於對角的角落,收集試體之位移與速度。經由Fourier轉換,將時間域的端 點速度轉至頻率域,藉由分析共振頻率,關聯其與等向性及異向性材料彈性常數之關 係。此外,本文亦使用COMSOL有限元素軟體,分析等向性線黏彈性材料之應力波傳 遞行為,以了解高阻尼材料為何無法使用共振超音波實驗量測。最後,兩相複合材料 含正勁度或負勁度之應力波相關問題,亦有所探討。本研究發現,因分析耗時,RUS code不宜分析頻率 400 kHz 以上的材料共振反應。當材料具高度異向性時,RUS code 的結果與COMSOL結果一致性較高。

Resonant ultrasound spectroscopy (RUS) is an efficient and accurate experimental method to determine the linear viscoelastic properties of solid materials. This research is motivated from the difficulty to implement the RUS experiment in two-dimensional (2D) specimens with plate-like geometry, and hence it is needed to develop numerical techniques to reduce the data. The rationale for the development of the RUS code is to implement the mathematical theory of high order finite difference (HOFD), and then to analyze 2D linear isotropic elastic materials, 2D linear anisotropic elastic materials, and 2D linear isotropic viscoelastic materials. The RUS code uses the HOFD scheme which is better in memory using, and COMSOL uses finite element method (FEM). Both were adopted in this study for verification. For isotropic, and anisotropic elasticity, the velocity and stress are obtained by giving the Ricker wavelet excitation on one corner of the thin plates. The HOFD scheme, five-stage forth-order of Runge-Kutta (RK4S5), was implemented during the calculation by using fortran 90. For linear viscoelastic, and composite material, the velocity and stress in time domain are obtained by using COMSOL software which is given Ricker wavelet too. Then the time history is converted into the frequency domain by using fourier transform. The identified resonant frequencies are compared with the results of the eigenfrequency analysis from COMSOL software. For viscoelastic materials, the time-dependent analysis needs to be run with longer time simulation, but the eigenfrequency analysis is needed the further study. This RUS code performs better for more anisotropic material and valid for analyzing materials with natural frequency below 400 kHz. Beside those things, RUS code is able to calculate the non-composite material with more than one domain for square and rectangular shape, and also able to collect the information in the nodal points.

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